{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T15:34:07Z","timestamp":1767108847356},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2011,3]]},"abstract":"<jats:p> The k th power of a graph G, denoted by G<jats:sup>k<\/jats:sup>, is a graph whose vertex set is V(G), two distinct vertices being adjacent in G<jats:sup>k<\/jats:sup> if and only if their distance in G is at most k. The hyper-Wiener index WW(G) of a graph G is defined as [Formula: see text], where d<jats:sub>G<\/jats:sub>(u,v) is the distance between vertices u and v in G. In this paper, the bounds on the hyper-Wiener index of the graph G<jats:sup>k<\/jats:sup> are given. The Nordhaus\u2013Gaddum-type inequality for the hyper-Wiener-index of the graph G<jats:sup>k<\/jats:sup> is also presented. <\/jats:p>","DOI":"10.1142\/s1793830911000973","type":"journal-article","created":{"date-parts":[[2011,4,14]],"date-time":"2011-04-14T09:45:47Z","timestamp":1302774347000},"page":"17-23","source":"Crossref","is-referenced-by-count":3,"title":["THE HYPER-WIENER INDEX OF THE k<font>th<\/font> POWER OF A GRAPH"],"prefix":"10.1142","volume":"03","author":[{"given":"WEIJUAN","family":"ZHANG","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Xinjiang Normal University, Urumqi, Xinjiang 830054, China"}]},{"given":"BAOYINDURENG","family":"WU","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang 830046, China"}]},{"given":"XINHUI","family":"AN","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang 830046, China"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2007.03.025"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-9659(02)00059-9"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1023\/A:1010767517079"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/S0009-2614(02)01343-X"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1021\/ci960139m"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0097-8485(99)00062-5"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1021\/ci00023a007"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-1280(03)00333-6"},{"key":"rf10","first-page":"65","volume":"35","author":"Linert W.","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.2307\/2306658"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/0009-2614(93)87094-J"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1021\/ja01193a005"},{"key":"rf14","first-page":"189","volume":"54","author":"Zhang L.","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/j.cplett.2004.06.117"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830911000973","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T01:32:16Z","timestamp":1565141536000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830911000973"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3]]},"references-count":15,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2012,4,5]]},"published-print":{"date-parts":[[2011,3]]}},"alternative-id":["10.1142\/S1793830911000973"],"URL":"https:\/\/doi.org\/10.1142\/s1793830911000973","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3]]}}}